Reaction selection

Once a muonic atom is created, various reactions can take place, which include muon decay, elastic scattering, inelastic scattering, muon transfer, muonic molecular formation followed by fusion or back decay, and muon capture (after transfer to a heavy element). Some of the theoretical input for density dependent reactions is given in terms of cross sections, but it is convenient to convert them to rates. For the process i:

where v _rel is the relative velocity between the projectile and the target, and n_i is the number density of the relevant target species. Inputs for other reactions are given by rates, some such as molecular formation, dependent on the density and/or collision velocity, while others such as muon decay independent of the above.

The simulation was done in an energy dependent manner, and for a given state of the projectile with a particular energy, the probability for ith reaction , out of m possible different reactions, is given by:

where is the reduced rate for each reaction, given by Eq. 5.1 for cross section inputs, or by

for input by rates, where C_i is the relative concentration of relevant species, is the target number density in the unit of liquid hydrogen atomic density cm^-3, and is the rate normalized to n₀. The processes such as muon decay and nuclear muon capture are independent of the target concentration C_i. For muon decay, for example, is , where is the free muon decay rate and Q_k the Huff factor in the kth element.